In California, who gets the assets when one dies without a Will?

That depends on several factors, including whether there is a surviving spouse or partner, and/or children and whether there is a  'recently' deceased spouse, and what type of property is involved:

From the Probate Code:

6401.  (a) As to community property, the intestate share of the
surviving spouse is the one-half of the community property that
belongs to the decedent under Section 100.
   (b) As to quasi-community property, the intestate share of the
surviving spouse is the one-half of the quasi-community property that
belongs to the decedent under Section 101.
   (c) As to separate property, the intestate share of the surviving
spouse or surviving domestic partner, as defined in subdivision (b)
of Section 37, is as follows:
   (1) The entire intestate estate if the decedent did not leave any
surviving issue, parent, brother, sister, or issue of a deceased
brother or sister.
   (2) One-half of the intestate estate in the following cases:
   (A) Where the decedent leaves only one child or the issue of one
deceased child.
   (B) Where the decedent leaves no issue but leaves a parent or
parents or their issue or the issue of either of them.
   (3) One-third of the intestate estate in the following cases:
   (A) Where the decedent leaves more than one child.
   (B) Where the decedent leaves one child and the issue of one or
more deceased children.
   (C) Where the decedent leaves issue of two or more deceased
children.


6402.  Except as provided in Section 6402.5, the part of the
intestate estate not passing to the surviving spouse or surviving
domestic partner, as defined in subdivision (b) of Section 37, under
Section 6401, or the entire intestate estate if there is no surviving
spouse or domestic partner, passes as follows:
   (a) To the issue of the decedent, the issue taking equally if they
are all of the same degree of kinship to the decedent, but if of
unequal degree those of more remote degree take in the manner
provided in Section 240.
   (b) If there is no surviving issue, to the decedent's parent or
parents equally.
   (c) If there is no surviving issue or parent, to the issue of the
parents or either of them, the issue taking equally if they are all
of the same degree of kinship to the decedent, but if of unequal
degree those of more remote degree take in the manner provided in
Section 240.
   (d) If there is no surviving issue, parent or issue of a parent,
but the decedent is survived by one or more grandparents or issue of
grandparents,  to the grandparent or grandparents equally, or to the
issue of  those grandparents if there is no surviving grandparent,
the issue taking equally if they are all of the same degree of
kinship to the decedent, but if of unequal degree those of more
remote degree take in the manner provided in Section 240.
   (e) If there is no surviving issue, parent or issue of a parent,
grandparent or issue of a grandparent, but the  decedent is survived
by the issue of a predeceased spouse, to  that issue, the issue
taking equally if they are all of the same degree of kinship to the
predeceased spouse, but if of unequal degree those of more remote
degree take in the manner provided in Section 240.
   (f) If there is no surviving issue, parent or issue of a parent,
grandparent or issue of a grandparent, or issue of a predeceased
spouse, but the decedent is  survived by next of kin, to the next of
kin in equal degree, but where there are two or more collateral
kindred in equal degree who claim through different ancestors, those
who claim through the nearest ancestor are preferred to those
claiming through an ancestor more remote.
   (g) If there is no surviving next of kin of the decedent and no
surviving issue of a predeceased spouse of the decedent, but the
decedent is survived by the parents of a predeceased spouse or the
issue of  those parents, to the parent or parents equally, or to the
issue of  those parents if both are deceased, the issue taking
equally if they are all of the same degree of kinship to the
predeceased spouse, but if of unequal degree those of more remote
degree take in the manner provided in Section 240.



6402.5.  (a) For purposes of distributing real property under this
section if the decedent had a predeceased spouse who died not more
than 15 years before the decedent and there is no surviving spouse or
issue of the decedent, the portion of the decedent's estate
attributable to the decedent's predeceased spouse passes as follows:

   (1) If the decedent is survived by issue of the predeceased
spouse, to the surviving issue of the predeceased spouse; if they are
all of the same degree of kinship to the predeceased spouse they
take equally, but if of unequal degree those of more remote degree
take in the manner provided in Section 240.
   (2) If there is no surviving issue of the predeceased spouse but
the decedent is survived by a parent or parents of the predeceased
spouse, to the predeceased spouse's surviving parent or parents
equally.
   (3) If there is no surviving issue or parent of the predeceased
spouse but the decedent is survived by issue of a parent of the
predeceased spouse, to the surviving issue of the parents of the
predeceased spouse or either of them, the issue taking equally if
they are all of the same degree of kinship to the predeceased spouse,
but if of unequal degree those of more remote degree take in the
manner provided in Section 240.
   (4) If the decedent is not survived by issue, parent, or issue of
a parent of  the predeceased spouse, to the next of kin of the
decedent in the manner provided in Section 6402.
   (5) If the portion of the decedent's estate attributable to the
decedent's predeceased spouse would otherwise escheat to the state
because there is no kin of  the decedent to take under Section 6402,
the portion of the decedent's estate attributable to the predeceased
spouse passes to the next of kin of the predeceased spouse who shall
take in the same manner as the next of kin of the decedent take under
Section 6402.
   (b) For purposes of distributing personal property under this
section if the decedent had a predeceased spouse who died not more
than five years before the decedent, and there is no surviving spouse
or issue of the decedent, the portion of the decedent's estate
attributable to the decedent's predeceased spouse passes  as follows:

   (1) If the decedent is survived by issue of the predeceased
spouse, to the surviving issue of the predeceased spouse; if they are
all of the same degree of kinship to the predeceased spouse they
take equally, but if of unequal degree those of more remote degree
take in the manner provided in Section 240.
   (2) If there is no surviving issue of the predeceased spouse but
the decedent  is survived by a parent or parents of the predeceased
spouse, to the predeceased spouse's surviving parent or parents
equally.
   (3) If there is no surviving issue or parent of the predeceased
spouse but the decedent is survived by issue of a parent of the
predeceased spouse, to the  surviving issue of the parents of the
predeceased spouse or either of them, the issue taking equally if
they are all of the same degree of kinship to the predeceased spouse,
but if of unequal degree those of more remote degree take in the
manner provided in Section 240.
   (4) If the decedent is not survived by issue, parent, or issue of
a parent of  the predeceased spouse, to the next of kin of the
decedent in the manner provided in Section 6402.
   (5) If the portion of the decedent's estate attributable to the
decedent's predeceased spouse would otherwise escheat to the state
because there is no kin of  the decedent to take under Section 6402,
the portion of the decedent's estate attributable to the predeceased
spouse passes to the next of kin of the predeceased spouse who shall
take in the same manner as the next of kin of the decedent take under
Section 6402.
   (c) For purposes of disposing of personal property under
subdivision (b), the claimant heir bears the burden of proof to show
the exact personal property to be disposed of to the heir.
   (d) For purposes of providing notice under any provision of this
code with respect to an estate that may include personal property
subject to distribution under subdivision (b), if the aggregate fair
market value of tangible and intangible personal property with a
written record of title or ownership in the estate is believed in
good faith by the petitioning party to be less than ten thousand
dollars ($10,000), the petitioning party need not give notice to the
issue or next of kin of the predeceased spouse.  If the personal
property is subsequently determined to have an aggregate fair market
value in excess of ten thousand dollars ($10,000), notice shall be
given to the issue or next of kin of the predeceased spouse as
provided by law.
   (e) For the purposes of disposing of property pursuant to
subdivision (b), "personal property" means that personal property in
which there is a written record of title or ownership and the value
of which in the aggregate is ten thousand dollars ($10,000) or more.