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HOUSTON — South Carolina-based development and management firm Greystar has begun leasing Ltd. Med Center, a newly built apartment community in Houston that totals 378 units, according to Apartments.com. Located near Texas Medical Center on the city’s south side, the property offers one- and two-bedroom units and amenities such as a pool, fitness center, dog park, resident lounge and a gaming area. Information on starting rents was not disclosed.