  A detailed study of vortices is presented in Ginzburg-Landau (or Abelian
Higgs) models with two complex scalars (order parameters) assuming a general
U(1)$\times$U(1) symmetric potential. Particular emphasis is given to the case,
when only one of the scalars obtains a vacuum expectation value (VEV). It is
found that for a significantly large domain in parameter space vortices with a
scalar field condensate in their core (condensate core, CC) coexist with
Abrikosov-Nielsen-Olesen (ANO) vortices. Importantly CC vortices are stable and
have lower energy than the ANO ones. Magnetic bags or giant vortices of the
order of 1000 flux quanta are favoured to form for the range of parameters
("strong couplings") appearing for the superconducting state of liquid metallic
hydrogen (LMH). Furthermore, it is argued that finite energy/unit length 1VEV
vortices are smoothly connected to fractional flux 2VEV ones. Stable, finite
energy CC-type vortices are also exhibited in the case when one of the scalar
fields is neutral.
