A way to optimize performance of relational row store databases is to reduce the row widths by vertically partitioning tables into table fractions in order to minimize the number of irrelevant columns/attributes read by each transaction. This paper considers vertical partitioning algorithms for relational row-store OLTP databases with an H-store-like architecture, meaning that we would like to maximize the number of single-sited transactions. We present a model for the vertical partitioning problem that, given a schema together with a vertical partitioning and a workload, estimates the costs (bytes read/written by storage layer access methods and bytes transferred between sites) of evaluating the workload on the given partitioning. The cost model allows for arbitrarily prioritizing load balancing of sites vs. total cost minimization. We show that finding a minimum-cost vertical partitioning in this model is NP-hard and present two algorithms returning solutions in which single-sitedness of read queries is preserved while allowing column replication (which may allow a drastically reduced cost compared to disjoint partitioning). The first algorithm is a quadratic integer program that finds optimal minimum-cost solutions with respect to the model, and the second algorithm is a more scalable heuristic based on simulated annealing. Experiments show that the algorithms can reduce the cost of the model objective by 37% when applied to the TPC-C benchmark and the heuristic is shown to obtain solutions with cost close to the ones found using the quadratic program.