Coannihilation effects in neutralino relic density calculations are examined for a full range of supersymmetry parameters including large tan β and large A0 for stau, chargino, stop and sbottom coannihilation with the neutralino. Supergravity models possessing grand unification with universal soft breaking (mSUGRA), models with nonuniversal soft breaking in the Higgs and third generation sparticles, and D-brane models with nonuniversal gaugino masses were analysed. Unlike low tanβ where m0 is generally small, stau coannihilation corridors with high tanβ are highly sensitive to A0, and large A0 allows m0 to become as large as 1TeV. Nonuniversal soft breaking models at high tanβ also allow the opening of a new annihilation channel through the schannel Z pole with acceptable relic density, allowing a new wide band in the m0 −m1/2 plane with m1/2 > ∼ 400 GeV and m0 rising to 1 TeV. The D-brane models considered possess stau coannihilations regions similar to mSUGRA, as well as small regions of chargino coannihilation. Neutralino-proton cross sections are analysed for all models and it is found that future detectors for halo wimps will be able to scan essentially the full parameter space with m1/2 < 1 TeV except for a region with μ < 0 where accidental cancellations occur when 5 < ∼ tan β < ∼ 30. Analytic explanations of much of the above phenomena are given. The above analyses include current LEP bounds on the Higgs mass, large tan β NLO correction to the b → sγ decay, and large tan β SUSY corrections to the b and τ masses.